924 lines
26 KiB
C
924 lines
26 KiB
C
#include <math.h>
|
|
#include <stdlib.h>
|
|
#include <string.h>
|
|
#include <stdio.h>
|
|
#include <complex.h>
|
|
#ifdef complex
|
|
#undef complex
|
|
#endif
|
|
#ifdef I
|
|
#undef I
|
|
#endif
|
|
|
|
#if defined(_WIN64)
|
|
typedef long long BLASLONG;
|
|
typedef unsigned long long BLASULONG;
|
|
#else
|
|
typedef long BLASLONG;
|
|
typedef unsigned long BLASULONG;
|
|
#endif
|
|
|
|
#ifdef LAPACK_ILP64
|
|
typedef BLASLONG blasint;
|
|
#if defined(_WIN64)
|
|
#define blasabs(x) llabs(x)
|
|
#else
|
|
#define blasabs(x) labs(x)
|
|
#endif
|
|
#else
|
|
typedef int blasint;
|
|
#define blasabs(x) abs(x)
|
|
#endif
|
|
|
|
typedef blasint integer;
|
|
|
|
typedef unsigned int uinteger;
|
|
typedef char *address;
|
|
typedef short int shortint;
|
|
typedef float real;
|
|
typedef double doublereal;
|
|
typedef struct { real r, i; } complex;
|
|
typedef struct { doublereal r, i; } doublecomplex;
|
|
#ifdef _MSC_VER
|
|
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
|
|
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
|
|
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
|
|
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
|
|
#else
|
|
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
|
|
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
|
|
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
|
|
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
|
|
#endif
|
|
#define pCf(z) (*_pCf(z))
|
|
#define pCd(z) (*_pCd(z))
|
|
typedef int logical;
|
|
typedef short int shortlogical;
|
|
typedef char logical1;
|
|
typedef char integer1;
|
|
|
|
#define TRUE_ (1)
|
|
#define FALSE_ (0)
|
|
|
|
/* Extern is for use with -E */
|
|
#ifndef Extern
|
|
#define Extern extern
|
|
#endif
|
|
|
|
/* I/O stuff */
|
|
|
|
typedef int flag;
|
|
typedef int ftnlen;
|
|
typedef int ftnint;
|
|
|
|
/*external read, write*/
|
|
typedef struct
|
|
{ flag cierr;
|
|
ftnint ciunit;
|
|
flag ciend;
|
|
char *cifmt;
|
|
ftnint cirec;
|
|
} cilist;
|
|
|
|
/*internal read, write*/
|
|
typedef struct
|
|
{ flag icierr;
|
|
char *iciunit;
|
|
flag iciend;
|
|
char *icifmt;
|
|
ftnint icirlen;
|
|
ftnint icirnum;
|
|
} icilist;
|
|
|
|
/*open*/
|
|
typedef struct
|
|
{ flag oerr;
|
|
ftnint ounit;
|
|
char *ofnm;
|
|
ftnlen ofnmlen;
|
|
char *osta;
|
|
char *oacc;
|
|
char *ofm;
|
|
ftnint orl;
|
|
char *oblnk;
|
|
} olist;
|
|
|
|
/*close*/
|
|
typedef struct
|
|
{ flag cerr;
|
|
ftnint cunit;
|
|
char *csta;
|
|
} cllist;
|
|
|
|
/*rewind, backspace, endfile*/
|
|
typedef struct
|
|
{ flag aerr;
|
|
ftnint aunit;
|
|
} alist;
|
|
|
|
/* inquire */
|
|
typedef struct
|
|
{ flag inerr;
|
|
ftnint inunit;
|
|
char *infile;
|
|
ftnlen infilen;
|
|
ftnint *inex; /*parameters in standard's order*/
|
|
ftnint *inopen;
|
|
ftnint *innum;
|
|
ftnint *innamed;
|
|
char *inname;
|
|
ftnlen innamlen;
|
|
char *inacc;
|
|
ftnlen inacclen;
|
|
char *inseq;
|
|
ftnlen inseqlen;
|
|
char *indir;
|
|
ftnlen indirlen;
|
|
char *infmt;
|
|
ftnlen infmtlen;
|
|
char *inform;
|
|
ftnint informlen;
|
|
char *inunf;
|
|
ftnlen inunflen;
|
|
ftnint *inrecl;
|
|
ftnint *innrec;
|
|
char *inblank;
|
|
ftnlen inblanklen;
|
|
} inlist;
|
|
|
|
#define VOID void
|
|
|
|
union Multitype { /* for multiple entry points */
|
|
integer1 g;
|
|
shortint h;
|
|
integer i;
|
|
/* longint j; */
|
|
real r;
|
|
doublereal d;
|
|
complex c;
|
|
doublecomplex z;
|
|
};
|
|
|
|
typedef union Multitype Multitype;
|
|
|
|
struct Vardesc { /* for Namelist */
|
|
char *name;
|
|
char *addr;
|
|
ftnlen *dims;
|
|
int type;
|
|
};
|
|
typedef struct Vardesc Vardesc;
|
|
|
|
struct Namelist {
|
|
char *name;
|
|
Vardesc **vars;
|
|
int nvars;
|
|
};
|
|
typedef struct Namelist Namelist;
|
|
|
|
#define abs(x) ((x) >= 0 ? (x) : -(x))
|
|
#define dabs(x) (fabs(x))
|
|
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
|
|
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
|
|
#define dmin(a,b) (f2cmin(a,b))
|
|
#define dmax(a,b) (f2cmax(a,b))
|
|
#define bit_test(a,b) ((a) >> (b) & 1)
|
|
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
|
|
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
|
|
|
|
#define abort_() { sig_die("Fortran abort routine called", 1); }
|
|
#define c_abs(z) (cabsf(Cf(z)))
|
|
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
|
|
#ifdef _MSC_VER
|
|
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
|
|
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/Cd(b)._Val[1]);}
|
|
#else
|
|
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
|
|
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
|
|
#endif
|
|
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
|
|
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
|
|
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
|
|
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
|
|
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
|
|
#define d_abs(x) (fabs(*(x)))
|
|
#define d_acos(x) (acos(*(x)))
|
|
#define d_asin(x) (asin(*(x)))
|
|
#define d_atan(x) (atan(*(x)))
|
|
#define d_atn2(x, y) (atan2(*(x),*(y)))
|
|
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
|
|
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
|
|
#define d_cos(x) (cos(*(x)))
|
|
#define d_cosh(x) (cosh(*(x)))
|
|
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
|
|
#define d_exp(x) (exp(*(x)))
|
|
#define d_imag(z) (cimag(Cd(z)))
|
|
#define r_imag(z) (cimagf(Cf(z)))
|
|
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
|
|
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
|
|
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
|
|
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
|
|
#define d_log(x) (log(*(x)))
|
|
#define d_mod(x, y) (fmod(*(x), *(y)))
|
|
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
|
|
#define d_nint(x) u_nint(*(x))
|
|
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
|
|
#define d_sign(a,b) u_sign(*(a),*(b))
|
|
#define r_sign(a,b) u_sign(*(a),*(b))
|
|
#define d_sin(x) (sin(*(x)))
|
|
#define d_sinh(x) (sinh(*(x)))
|
|
#define d_sqrt(x) (sqrt(*(x)))
|
|
#define d_tan(x) (tan(*(x)))
|
|
#define d_tanh(x) (tanh(*(x)))
|
|
#define i_abs(x) abs(*(x))
|
|
#define i_dnnt(x) ((integer)u_nint(*(x)))
|
|
#define i_len(s, n) (n)
|
|
#define i_nint(x) ((integer)u_nint(*(x)))
|
|
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
|
|
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
|
|
#define pow_si(B,E) spow_ui(*(B),*(E))
|
|
#define pow_ri(B,E) spow_ui(*(B),*(E))
|
|
#define pow_di(B,E) dpow_ui(*(B),*(E))
|
|
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
|
|
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
|
|
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
|
|
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
|
|
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
|
|
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
|
|
#define sig_die(s, kill) { exit(1); }
|
|
#define s_stop(s, n) {exit(0);}
|
|
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
|
|
#define z_abs(z) (cabs(Cd(z)))
|
|
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
|
|
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
|
|
#define myexit_() break;
|
|
#define mycycle_() continue;
|
|
#define myceiling_(w) {ceil(w)}
|
|
#define myhuge_(w) {HUGE_VAL}
|
|
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
|
|
#define mymaxloc_(w,s,e,n) dmaxloc_(w,*(s),*(e),n)
|
|
|
|
/* procedure parameter types for -A and -C++ */
|
|
|
|
#define F2C_proc_par_types 1
|
|
#ifdef __cplusplus
|
|
typedef logical (*L_fp)(...);
|
|
#else
|
|
typedef logical (*L_fp)();
|
|
#endif
|
|
|
|
static float spow_ui(float x, integer n) {
|
|
float pow=1.0; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x = 1/x;
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow *= x;
|
|
if(u >>= 1) x *= x;
|
|
else break;
|
|
}
|
|
}
|
|
return pow;
|
|
}
|
|
static double dpow_ui(double x, integer n) {
|
|
double pow=1.0; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x = 1/x;
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow *= x;
|
|
if(u >>= 1) x *= x;
|
|
else break;
|
|
}
|
|
}
|
|
return pow;
|
|
}
|
|
#ifdef _MSC_VER
|
|
static _Fcomplex cpow_ui(complex x, integer n) {
|
|
complex pow={1.0,0.0}; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow.r *= x.r, pow.i *= x.i;
|
|
if(u >>= 1) x.r *= x.r, x.i *= x.i;
|
|
else break;
|
|
}
|
|
}
|
|
_Fcomplex p={pow.r, pow.i};
|
|
return p;
|
|
}
|
|
#else
|
|
static _Complex float cpow_ui(_Complex float x, integer n) {
|
|
_Complex float pow=1.0; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x = 1/x;
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow *= x;
|
|
if(u >>= 1) x *= x;
|
|
else break;
|
|
}
|
|
}
|
|
return pow;
|
|
}
|
|
#endif
|
|
#ifdef _MSC_VER
|
|
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
|
|
_Dcomplex pow={1.0,0.0}; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
|
|
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
|
|
else break;
|
|
}
|
|
}
|
|
_Dcomplex p = {pow._Val[0], pow._Val[1]};
|
|
return p;
|
|
}
|
|
#else
|
|
static _Complex double zpow_ui(_Complex double x, integer n) {
|
|
_Complex double pow=1.0; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x = 1/x;
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow *= x;
|
|
if(u >>= 1) x *= x;
|
|
else break;
|
|
}
|
|
}
|
|
return pow;
|
|
}
|
|
#endif
|
|
static integer pow_ii(integer x, integer n) {
|
|
integer pow; unsigned long int u;
|
|
if (n <= 0) {
|
|
if (n == 0 || x == 1) pow = 1;
|
|
else if (x != -1) pow = x == 0 ? 1/x : 0;
|
|
else n = -n;
|
|
}
|
|
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
|
|
u = n;
|
|
for(pow = 1; ; ) {
|
|
if(u & 01) pow *= x;
|
|
if(u >>= 1) x *= x;
|
|
else break;
|
|
}
|
|
}
|
|
return pow;
|
|
}
|
|
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
|
|
{
|
|
double m; integer i, mi;
|
|
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
|
|
if (w[i-1]>m) mi=i ,m=w[i-1];
|
|
return mi-s+1;
|
|
}
|
|
static integer smaxloc_(float *w, integer s, integer e, integer *n)
|
|
{
|
|
float m; integer i, mi;
|
|
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
|
|
if (w[i-1]>m) mi=i ,m=w[i-1];
|
|
return mi-s+1;
|
|
}
|
|
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
|
|
/* Subroutine */ int dlaqp2rk_(integer *m, integer *n, integer *nrhs, integer
|
|
*ioffset, integer *kmax, doublereal *abstol, doublereal *reltol,
|
|
integer *kp1, doublereal *maxc2nrm, doublereal *a, integer *lda,
|
|
integer *k, doublereal *maxc2nrmk, doublereal *relmaxc2nrmk, integer *
|
|
jpiv, doublereal *tau, doublereal *vn1, doublereal *vn2, doublereal *
|
|
work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1, i__2, i__3;
|
|
doublereal d__1, d__2;
|
|
|
|
/* Local variables */
|
|
doublereal aikk, temp;
|
|
extern doublereal dnrm2_(integer *, doublereal *, integer *);
|
|
doublereal temp2;
|
|
integer i__, j;
|
|
doublereal tol3z;
|
|
integer jmaxc2nrm;
|
|
extern /* Subroutine */ int dlarf_(char *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *);
|
|
integer itemp;
|
|
extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *);
|
|
integer minmnfact;
|
|
doublereal myhugeval;
|
|
integer minmnupdt, kk;
|
|
extern doublereal dlamch_(char *);
|
|
integer kp;
|
|
extern /* Subroutine */ int dlarfg_(integer *, doublereal *, doublereal *,
|
|
integer *, doublereal *);
|
|
extern integer idamax_(integer *, doublereal *, integer *);
|
|
extern logical disnan_(doublereal *);
|
|
|
|
|
|
/* -- LAPACK auxiliary routine -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Initialize INFO */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--jpiv;
|
|
--tau;
|
|
--vn1;
|
|
--vn2;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
/* MINMNFACT in the smallest dimension of the submatrix */
|
|
/* A(IOFFSET+1:M,1:N) to be factorized. */
|
|
|
|
/* MINMNUPDT is the smallest dimension */
|
|
/* of the subarray A(IOFFSET+1:M,1:N+NRHS) to be udated, which */
|
|
/* contains the submatrices A(IOFFSET+1:M,1:N) and */
|
|
/* B(IOFFSET+1:M,1:NRHS) as column blocks. */
|
|
|
|
/* Computing MIN */
|
|
i__1 = *m - *ioffset;
|
|
minmnfact = f2cmin(i__1,*n);
|
|
/* Computing MIN */
|
|
i__1 = *m - *ioffset, i__2 = *n + *nrhs;
|
|
minmnupdt = f2cmin(i__1,i__2);
|
|
*kmax = f2cmin(*kmax,minmnfact);
|
|
tol3z = sqrt(dlamch_("Epsilon"));
|
|
myhugeval = dlamch_("Overflow");
|
|
|
|
/* Compute the factorization, KK is the lomn loop index. */
|
|
|
|
i__1 = *kmax;
|
|
for (kk = 1; kk <= i__1; ++kk) {
|
|
|
|
i__ = *ioffset + kk;
|
|
|
|
if (i__ == 1) {
|
|
|
|
/* ============================================================ */
|
|
|
|
/* We are at the first column of the original whole matrix A, */
|
|
/* therefore we use the computed KP1 and MAXC2NRM from the */
|
|
/* main routine. */
|
|
|
|
kp = *kp1;
|
|
|
|
/* ============================================================ */
|
|
|
|
} else {
|
|
|
|
/* ============================================================ */
|
|
|
|
/* Determine the pivot column in KK-th step, i.e. the index */
|
|
/* of the column with the maximum 2-norm in the */
|
|
/* submatrix A(I:M,K:N). */
|
|
|
|
i__2 = *n - kk + 1;
|
|
kp = kk - 1 + idamax_(&i__2, &vn1[kk], &c__1);
|
|
|
|
/* Determine the maximum column 2-norm and the relative maximum */
|
|
/* column 2-norm of the submatrix A(I:M,KK:N) in step KK. */
|
|
/* RELMAXC2NRMK will be computed later, after somecondition */
|
|
/* checks on MAXC2NRMK. */
|
|
|
|
*maxc2nrmk = vn1[kp];
|
|
|
|
/* ============================================================ */
|
|
|
|
/* Check if the submatrix A(I:M,KK:N) contains NaN, and set */
|
|
/* INFO parameter to the column number, where the first NaN */
|
|
/* is found and return from the routine. */
|
|
/* We need to check the condition only if the */
|
|
/* column index (same as row index) of the original whole */
|
|
/* matrix is larger than 1, since the condition for whole */
|
|
/* original matrix is checked in the main routine. */
|
|
|
|
if (disnan_(maxc2nrmk)) {
|
|
|
|
/* Set K, the number of factorized columns. */
|
|
/* that are not zero. */
|
|
|
|
*k = kk - 1;
|
|
*info = *k + kp;
|
|
|
|
/* Set RELMAXC2NRMK to NaN. */
|
|
|
|
*relmaxc2nrmk = *maxc2nrmk;
|
|
|
|
/* Array TAU(K+1:MINMNFACT) is not set and contains */
|
|
/* undefined elements. */
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* ============================================================ */
|
|
|
|
/* Quick return, if the submatrix A(I:M,KK:N) is */
|
|
/* a zero matrix. */
|
|
/* We need to check the condition only if the */
|
|
/* column index (same as row index) of the original whole */
|
|
/* matrix is larger than 1, since the condition for whole */
|
|
/* original matrix is checked in the main routine. */
|
|
|
|
if (*maxc2nrmk == 0.) {
|
|
|
|
/* Set K, the number of factorized columns. */
|
|
/* that are not zero. */
|
|
|
|
*k = kk - 1;
|
|
*relmaxc2nrmk = 0.;
|
|
|
|
/* Set TAUs corresponding to the columns that were not */
|
|
/* factorized to ZERO, i.e. set TAU(KK:MINMNFACT) to ZERO. */
|
|
|
|
i__2 = minmnfact;
|
|
for (j = kk; j <= i__2; ++j) {
|
|
tau[j] = 0.;
|
|
}
|
|
|
|
/* Return from the routine. */
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
/* ============================================================ */
|
|
|
|
/* Check if the submatrix A(I:M,KK:N) contains Inf, */
|
|
/* set INFO parameter to the column number, where */
|
|
/* the first Inf is found plus N, and continue */
|
|
/* the computation. */
|
|
/* We need to check the condition only if the */
|
|
/* column index (same as row index) of the original whole */
|
|
/* matrix is larger than 1, since the condition for whole */
|
|
/* original matrix is checked in the main routine. */
|
|
|
|
if (*info == 0 && *maxc2nrmk > myhugeval) {
|
|
*info = *n + kk - 1 + kp;
|
|
}
|
|
|
|
/* ============================================================ */
|
|
|
|
/* Test for the second and third stopping criteria. */
|
|
/* NOTE: There is no need to test for ABSTOL >= ZERO, since */
|
|
/* MAXC2NRMK is non-negative. Similarly, there is no need */
|
|
/* to test for RELTOL >= ZERO, since RELMAXC2NRMK is */
|
|
/* non-negative. */
|
|
/* We need to check the condition only if the */
|
|
/* column index (same as row index) of the original whole */
|
|
/* matrix is larger than 1, since the condition for whole */
|
|
/* original matrix is checked in the main routine. */
|
|
*relmaxc2nrmk = *maxc2nrmk / *maxc2nrm;
|
|
|
|
if (*maxc2nrmk <= *abstol || *relmaxc2nrmk <= *reltol) {
|
|
|
|
/* Set K, the number of factorized columns. */
|
|
|
|
*k = kk - 1;
|
|
|
|
/* Set TAUs corresponding to the columns that were not */
|
|
/* factorized to ZERO, i.e. set TAU(KK:MINMNFACT) to ZERO. */
|
|
|
|
i__2 = minmnfact;
|
|
for (j = kk; j <= i__2; ++j) {
|
|
tau[j] = 0.;
|
|
}
|
|
|
|
/* Return from the routine. */
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
/* ============================================================ */
|
|
|
|
/* End ELSE of IF(I.EQ.1) */
|
|
|
|
}
|
|
|
|
/* =============================================================== */
|
|
|
|
/* If the pivot column is not the first column of the */
|
|
/* subblock A(1:M,KK:N): */
|
|
/* 1) swap the KK-th column and the KP-th pivot column */
|
|
/* in A(1:M,1:N); */
|
|
/* 2) copy the KK-th element into the KP-th element of the partial */
|
|
/* and exact 2-norm vectors VN1 and VN2. ( Swap is not needed */
|
|
/* for VN1 and VN2 since we use the element with the index */
|
|
/* larger than KK in the next loop step.) */
|
|
/* 3) Save the pivot interchange with the indices relative to the */
|
|
/* the original matrix A, not the block A(1:M,1:N). */
|
|
|
|
if (kp != kk) {
|
|
dswap_(m, &a[kp * a_dim1 + 1], &c__1, &a[kk * a_dim1 + 1], &c__1);
|
|
vn1[kp] = vn1[kk];
|
|
vn2[kp] = vn2[kk];
|
|
itemp = jpiv[kp];
|
|
jpiv[kp] = jpiv[kk];
|
|
jpiv[kk] = itemp;
|
|
}
|
|
|
|
/* Generate elementary reflector H(KK) using the column A(I:M,KK), */
|
|
/* if the column has more than one element, otherwise */
|
|
/* the elementary reflector would be an identity matrix, */
|
|
/* and TAU(KK) = ZERO. */
|
|
|
|
if (i__ < *m) {
|
|
i__2 = *m - i__ + 1;
|
|
dlarfg_(&i__2, &a[i__ + kk * a_dim1], &a[i__ + 1 + kk * a_dim1], &
|
|
c__1, &tau[kk]);
|
|
} else {
|
|
tau[kk] = 0.;
|
|
}
|
|
|
|
/* Check if TAU(KK) contains NaN, set INFO parameter */
|
|
/* to the column number where NaN is found and return from */
|
|
/* the routine. */
|
|
/* NOTE: There is no need to check TAU(KK) for Inf, */
|
|
/* since DLARFG cannot produce TAU(KK) or Householder vector */
|
|
/* below the diagonal containing Inf. Only BETA on the diagonal, */
|
|
/* returned by DLARFG can contain Inf, which requires */
|
|
/* TAU(KK) to contain NaN. Therefore, this case of generating Inf */
|
|
/* by DLARFG is covered by checking TAU(KK) for NaN. */
|
|
|
|
if (disnan_(&tau[kk])) {
|
|
*k = kk - 1;
|
|
*info = kk;
|
|
|
|
/* Set MAXC2NRMK and RELMAXC2NRMK to NaN. */
|
|
|
|
*maxc2nrmk = tau[kk];
|
|
*relmaxc2nrmk = tau[kk];
|
|
|
|
/* Array TAU(KK:MINMNFACT) is not set and contains */
|
|
/* undefined elements, except the first element TAU(KK) = NaN. */
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Apply H(KK)**T to A(I:M,KK+1:N+NRHS) from the left. */
|
|
/* ( If M >= N, then at KK = N there is no residual matrix, */
|
|
/* i.e. no columns of A to update, only columns of B. */
|
|
/* If M < N, then at KK = M-IOFFSET, I = M and we have a */
|
|
/* one-row residual matrix in A and the elementary */
|
|
/* reflector is a unit matrix, TAU(KK) = ZERO, i.e. no update */
|
|
/* is needed for the residual matrix in A and the */
|
|
/* right-hand-side-matrix in B. */
|
|
/* Therefore, we update only if */
|
|
/* KK < MINMNUPDT = f2cmin(M-IOFFSET, N+NRHS) */
|
|
/* condition is satisfied, not only KK < N+NRHS ) */
|
|
|
|
if (kk < minmnupdt) {
|
|
aikk = a[i__ + kk * a_dim1];
|
|
a[i__ + kk * a_dim1] = 1.;
|
|
i__2 = *m - i__ + 1;
|
|
i__3 = *n + *nrhs - kk;
|
|
dlarf_("Left", &i__2, &i__3, &a[i__ + kk * a_dim1], &c__1, &tau[
|
|
kk], &a[i__ + (kk + 1) * a_dim1], lda, &work[1]);
|
|
a[i__ + kk * a_dim1] = aikk;
|
|
}
|
|
|
|
if (kk < minmnfact) {
|
|
|
|
/* Update the partial column 2-norms for the residual matrix, */
|
|
/* only if the residual matrix A(I+1:M,KK+1:N) exists, i.e. */
|
|
/* when KK < f2cmin(M-IOFFSET, N). */
|
|
|
|
i__2 = *n;
|
|
for (j = kk + 1; j <= i__2; ++j) {
|
|
if (vn1[j] != 0.) {
|
|
|
|
/* NOTE: The following lines follow from the analysis in */
|
|
/* Lapack Working Note 176. */
|
|
|
|
/* Computing 2nd power */
|
|
d__2 = (d__1 = a[i__ + j * a_dim1], abs(d__1)) / vn1[j];
|
|
temp = 1. - d__2 * d__2;
|
|
temp = f2cmax(temp,0.);
|
|
/* Computing 2nd power */
|
|
d__1 = vn1[j] / vn2[j];
|
|
temp2 = temp * (d__1 * d__1);
|
|
if (temp2 <= tol3z) {
|
|
|
|
/* Compute the column 2-norm for the partial */
|
|
/* column A(I+1:M,J) by explicitly computing it, */
|
|
/* and store it in both partial 2-norm vector VN1 */
|
|
/* and exact column 2-norm vector VN2. */
|
|
|
|
i__3 = *m - i__;
|
|
vn1[j] = dnrm2_(&i__3, &a[i__ + 1 + j * a_dim1], &
|
|
c__1);
|
|
vn2[j] = vn1[j];
|
|
|
|
} else {
|
|
|
|
/* Update the column 2-norm for the partial */
|
|
/* column A(I+1:M,J) by removing one */
|
|
/* element A(I,J) and store it in partial */
|
|
/* 2-norm vector VN1. */
|
|
|
|
vn1[j] *= sqrt(temp);
|
|
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
/* End factorization loop */
|
|
|
|
}
|
|
|
|
/* If we reached this point, all colunms have been factorized, */
|
|
/* i.e. no condition was triggered to exit the routine. */
|
|
/* Set the number of factorized columns. */
|
|
|
|
*k = *kmax;
|
|
|
|
/* We reached the end of the loop, i.e. all KMAX columns were */
|
|
/* factorized, we need to set MAXC2NRMK and RELMAXC2NRMK before */
|
|
/* we return. */
|
|
|
|
if (*k < minmnfact) {
|
|
|
|
i__1 = *n - *k;
|
|
jmaxc2nrm = *k + idamax_(&i__1, &vn1[*k + 1], &c__1);
|
|
*maxc2nrmk = vn1[jmaxc2nrm];
|
|
|
|
if (*k == 0) {
|
|
*relmaxc2nrmk = 1.;
|
|
} else {
|
|
*relmaxc2nrmk = *maxc2nrmk / *maxc2nrm;
|
|
}
|
|
|
|
} else {
|
|
*maxc2nrmk = 0.;
|
|
*relmaxc2nrmk = 0.;
|
|
}
|
|
|
|
/* We reached the end of the loop, i.e. all KMAX columns were */
|
|
/* factorized, set TAUs corresponding to the columns that were */
|
|
/* not factorized to ZERO, i.e. TAU(K+1:MINMNFACT) set to ZERO. */
|
|
|
|
i__1 = minmnfact;
|
|
for (j = *k + 1; j <= i__1; ++j) {
|
|
tau[j] = 0.;
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of DLAQP2RK */
|
|
|
|
} /* dlaqp2rk_ */
|
|
|